Advertisement

The concentration-frequency distribution

  • Michel M. Benarie
Part of the Air Pollution Problems Series book series (AIRPP)

Abstract

The histogram of urban air pollutant concentrations sampled over any given time span (1 min, 1 h, 24 h, etc.) is quite skew. There are only a few near-zero values, but afterwards the frequency increases sharply, only to decrease again gradually towards the higher concentrations. A large number of skew distribution functions known in statistics can be fitted to such data: Poisson (Wipperman, 1966); negative binomial (Prinz and Stratmann, 1966); Weibull (Barlow, 1971; Curran and Frank, 1975; Tsukatani and Shoyi, 1977); exponential (Barry, 1971; Scriven, 1971; Curran and Frank, 1975); gamma (Pearson IV) and Pearson VI (Lynn, 1972); beta (Pearson I) (Lynn, 1972; Graedel et al. 1974); three-parameter log-normal (Mage, 1975; Larsen, 1977a,b). Pollack (1973, 1975) demonstrated that there is a fundamental similarity among these distributions when utilised to fit air quality data. Benarie (1971) (see also chapter 15) proved that in two limiting cases the concentrations are, as a very good approximation, log-normal. One of these cases is the concentration distribution due to the single point source; the other is the concentration distribution of the area source, when the number of identifiable individual sources in any direction is greater than 10 (homogeneous area source). When the receptor is influenced by a relatively small number of individual sources, deviations from the log-normal appear, and the distribution approaches one or other of the skew distributions quoted above.

Keywords

Pollutant Concentration Source Reduction Source Factor Interrelate Effect Single Point Source 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchinson, J., and Brown, J. A. C. (1969). The Log-normal Distribution, Cambridge Univ. Press, Cambridge, England, 176 pp.Google Scholar
  2. Barlow, R. E. (1971). Average time and maxima for air pollution concentration. Operations Res. Cent., Univ. Calif, Berkeley, Calif., Rep., No. ORC-71–17 (Natl Tech. Inf. Serv., No. NTIS AD-729–413)Google Scholar
  3. Barry, P. J. (1971). Use of argon-41 to study the dispersion of stack effluents. Proc. Symp. Nucl. Tech. Environ. Pollut., Int. At. Energy Agency, Vienna, pp. 241–53Google Scholar
  4. Benarie, M. M. (1971). About the validity of log-normal distribution of pollutant concentrations. Proc. 2nd Clean Air Congr., Washington, D.C., 6 to 10 December 1970 (eds H. M. Englund and W. T. Beery), Academic Press, New York, pp. 68–70 (in French)Google Scholar
  5. Coenen, W. (1976). Beschreibung des zeitlichen Verhaltens von Schadstoffkonzentrationen durch einen stetigen Markoffprozess. Staub, 36, 240–8 (in German)Google Scholar
  6. Curran, C. T., and Frank, H. N. (1975). Assessing the validity of log-normal model when predicting maximum air pollution concentrations. Proc. 68th Annu. Meet. Air Pollut. Control Assoc., Boston, Mass., 15 to 20 June 1975, Paper, No. 75–51.3, 17 pp.Google Scholar
  7. Gifford, F. A. (1972). The form of the frequency distribution of air pollution concentrations. Proc. Symp. Stat. Aspects Air Quality Data, Chapel Hill, N.C., 9 to 10 November 1972, US Environ. Prot. Agency, Publ., No. EPA–650/4–74–038, pp. 3–1–3–7Google Scholar
  8. Gould, G. (1961). The statistical analysis and interpretation of dustfall data. Proc. 54th Annu. Meet. Air Pollut. Control Assoc., New York, N. Y.Google Scholar
  9. Graedel, T. E., Kleiner, B., and Patterson, C. C. (1974). Measurements of extreme concentration of tropospheric hydrogen sulphide J. Geophys. Res., 79, 44–67Google Scholar
  10. Hunt, W. F., Jr. (1972). The precision associated with sampling frequency of log-normally distributed air pollution measurements. J. Air Pollut. Control Assoc., 22, 687–91CrossRefGoogle Scholar
  11. Inoue, R., and Watanabe, Y. (1977). Statistical properties of sulphur dioxide concentrations at continuous monitoring stations in Japan. Proc. 4th Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 150–2Google Scholar
  12. Jost, D., Kaller, R., Markush, H., and Rudolf, W. (1974). Analysis of 6 years’ continuous air pollution surveillance. Automatic Air Quality Monitoring Systems (ed. T. Schneider) Elsevier, Amsterdam, pp. 251–260Google Scholar
  13. Kahn, H. D. (1973). Note on the distribution of air pollutants. J. Air Pollut. Control Assoc., 23, 973CrossRefGoogle Scholar
  14. Knox, J. B., and Pollack, R. I. (1972). An investigation of the frequency distributions of surface air pollutant concentrations. Proc. Symp. Stat. Aspects Air Quality Data, Chapel Hill, N.C., 9 to 10 November 1972, US Environ. Prot. Agency, Publ., No. EPA–650/4–74–038, pp. 9–10–9–17Google Scholar
  15. Kretzschmar, J. G. (1977). Comments on ‘On determining the statistical parameters for pollution concentration from a truncated data set’ by Kushner, E. J., Atm. Env.,11, 866CrossRefGoogle Scholar
  16. Kushner, E. J. (1976). On determining the statistical parameters for pollution concentration from a truncated data set. Atm. Env.,10, 975–9CrossRefGoogle Scholar
  17. Larsen, R. I. (1961). A method for determining source reduction required to meet air quality standards. J. Air Pollut. Control Assoc.,11, 71–6CrossRefGoogle Scholar
  18. Larsen, R. I. (1964). United States air quality. Arch. Environ. Health,8, 325–33CrossRefGoogle Scholar
  19. Larsen, R. I. (1969). A new mathematical model of air pollutant concentration, averaging time and frequency. J. Air Pollut. Control Assoc.,19, 24–30CrossRefGoogle Scholar
  20. Larsen, R. I. (1971). A mathematical model for relating air quality measurements to air quality standards. US Environ. Prot. Agency, Publ., No. AP-89, 56 pp.Google Scholar
  21. Larsen, R. I. (1973). An air quality data analysis system for interrelating effects, standards and needed source reduction. J. Air Pollut. Control Assoc., 23, 933–40CrossRefGoogle Scholar
  22. Larsen, R. I. (1974). An air quality data analysis system for interrelating effects, standards and needed source reductions, part 2. J. Air Pollut. Control Assoc.,24, 551–8CrossRefGoogle Scholar
  23. Larsen, R. I. (1975). Personal communicationGoogle Scholar
  24. Larsen, R. I. (1977a). An air quality data analysis system for interrelating effects, standards and needed source reductions. J. Air Pollut. Control Assoc., 27, 454–9CrossRefGoogle Scholar
  25. Larsen, R. I. (1977b). An air quality data analysis system for interrelating effects, standards and needed source reductions, a summary. Proc. 4th Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 322–5Google Scholar
  26. Larsen, R. I., Benson, F. B., and Jutze, G. A. (1965). Improving the dynamic response of continuous air pollutant measurements with a computer. J. Air Pollut. Control Assoc.,15, 19–22CrossRefGoogle Scholar
  27. Larsen, R. I., Zimmer, C. E., Lynn, D. A., and Blemel, K. G. (1967). Analysing air pollutant concentration and dosage data. J. Air Pollut. Control Assoc.,17, 85–93CrossRefGoogle Scholar
  28. Lynn, D. A. (1972). Fitting curves to urban suspended particulate data. Proc. Symp. Stat. Aspects Air Quality Data, Chapel Hill, N.C., 9 to 10 November 1977, US Environ. Prot. Agency, Publ., No. EPA–650/4–74–038, pp. 13–1–13–28Google Scholar
  29. McGuire, T., and Noll, K. E. (1971). Relationship between concentrations of atmospheric pollutants and averaging time. Atmos. Environ.,5, 291–8CrossRefGoogle Scholar
  30. Mage, T. D. (1975). An improved statistical model for analysing air pollution concentration data. Proc. 68th Annu. Meet. Air Pollut. Control Assoc., Boston, Mass., 15 to 20 June 1975, Paper, No. 57–51.4, 28 pp.Google Scholar
  31. Marcus, A. H. (1972). A stochastic model for estimating pollutant exposure by means of air quality data. Proc. Symp. Stat. Aspects Air Quality Data, Chapel Hill, N.C., 9 to 10 November 1972, US Environ. Prot. Agency, Publ., No. EPA–650/4–74–038, pp. 7–1–7–15Google Scholar
  32. Milokay, P. G. (1972). Environmental applications of the Weibull distribution function: oil pollution. Science,176, 1019–21CrossRefGoogle Scholar
  33. de Nevers, N., Lee, K. W., and Frank, N. H. (1977). Extreme values in TSP distribution functions. J. Air Pollut. Control Assoc.,27, 995–1000CrossRefGoogle Scholar
  34. Pollack, R. I. (1973). Studies of pollutant concentration frequency distributions. Univ. Calif., Livermore, Calif., Thesis, 82 pp.Google Scholar
  35. Pollack, R. I. (1975). Studies of pollutant concentration frequency distributions. US Environ.Prot. Agency, Publ., No. EPA–650/4–75–004, 82 pp. (Reprint of Pollack (1973))Google Scholar
  36. Possanzini, M., and Liberti, A. (1972). Mathematical model for the evaluation of frequency distribution of concentrations of an atmospheric pollutant. Inquinamento,14, 23–27 (in Italian)Google Scholar
  37. Prinz, B., and Stratman, H. (1966). The statistics of propagation conditions in the light of continuous concentration measurements of gaseous pollutants. Staub,26, 4–12Google Scholar
  38. Scriven, R. A. (1971). Use of argon-41 to study the dispersion of stack effluents. Proc. Symp. Nucl. Tech. Environ. Pollut., Int. At. Energy Agency, Vienna, pp. 254–5Google Scholar
  39. Shoyi, H., and Tsukatani, T. (1973). Statistical model of air pollutant concentration and its application to the air quality standards. Atmos. Environ.,7, 485–501CrossRefGoogle Scholar
  40. Shoyi, H. (1975). Statistical model of air pollutant concentration. Kansai Univ., Technol. Rep., No. 17, pp. 121–31Google Scholar
  41. Singapurwalla, N. D. (1972). Extreme values from a lognormal law with applications to air pollution problems. Technometrics,14, 703CrossRefGoogle Scholar
  42. Stern, A. C. (1969). The systems approach to air pollution control. Proc. Clean Air Soc. Aust. N.Z. Clean Air Conf., vol.2, pp. 2.4.1–2. 4. 22Google Scholar
  43. Tsukatani, T., and Shoyi, H. (1977). Statistical model of air pollutant concentration. Proc. 4th Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 315–17Google Scholar
  44. United States Government (1958). Air pollution measurements of the national air sampling network, analyses of suspended particulates, 1953 to 1957. Dep. Health Educ. Welfare, Publ. Health Serv., Publ., No. 637, p. 245Google Scholar
  45. Wipperman, F. (1966). On the distribution of concentration fluctuations of a harmful gas propagating in the atmosphere. Unpublished MS, 17 pp.Google Scholar
  46. Zimmer, C. E., and Larsen, R. I. (1965). Calculating air quality and its control. J. Air Pollut. Control Assoc.,15, 565–72CrossRefGoogle Scholar
  47. Zimmer, C. E., Tabor, E. C., and Stern, A. C. (1959). Particulate pollutants in the air of the United States. J. Air Pollut. Control Assoc.,9, 136–40CrossRefGoogle Scholar

Copyright information

© Michel M. Benarie 1980

Authors and Affiliations

  • Michel M. Benarie
    • 1
  1. 1.Institut National de Recherche Chimique AppliquéeVert-le-PetitFrance

Personalised recommendations